@article {fall2009foliations, title = {Foliations of small tubes in Riemannian manifolds by capillary minimal discs}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {70}, number = {12}, year = {2009}, pages = {4422{\textendash}4440}, publisher = {Elsevier}, abstract = {

Letting\ Γ\ be an embedded curve in a Riemannian manifold\ M, we prove the existence of minimal disc-type surfaces centered at\ Γinside the surface of revolution of\ M\ around\ Γ, having small radius, and intersecting it with constant angles. In particular we obtain that small tubular neighborhoods can be foliated by minimal discs.

}, doi = {10.1016/j.na.2008.10.024}, url = {https://doi.org/10.1016/j.na.2008.10.024}, author = {Fall, Mouhamed Moustapha and Mercuri, Carlo} } @article {fall2009minimal, title = {Minimal disc-type surfaces embedded in a perturbed cylinder}, journal = {Differential and Integral Equations}, volume = {22}, number = {11/12}, year = {2009}, pages = {1115{\textendash}1124}, publisher = {Khayyam Publishing, Inc.}, abstract = {

In the present note we deal with small perturbations of an infinite cylinder in the 3D euclidian space. We find minimal disc-type surfaces embedded in the cylinder and intersecting its boundary perpendicularly. The existence and localization of those minimal discs is a consequence of a non-degeneracy condition for the critical points of a functional related to the oscillations of the cylinder from the flat configuration.

}, url = {https://projecteuclid.org/euclid.die/1356019407}, author = {Fall, Mouhamed Moustapha and Mercuri, Carlo} }